A Free-Space Measurement Method for the Low-Loss Dielectric Characterization Without Prior Need for Sample Thickness Data

Abstract

A free-space measurement method is presented for the characterization of low-loss dielectric materials at millimeter-wave frequencies that does not require any assumption of a priori knowledge of the sample thickness. The method first employs only maximal and minimal envelopes of measured transmission scattering parameters to determine the real part ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ' of the permittivity of test materials. Subsequently, the thickness of the sample is estimated from ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ' and frequencies for maximal and minimal peaks of the transmission scattering parameter. The calculation of the imaginary part ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> " of the permittivity then easily follows. Our method is examined by measuring two cross-linked polystyrene samples, one polytetrafluoroethylene sample and one polymethylpentene sample in the frequency range of 220-325 GHz at the incident angles of 0°, 10°, 20°, and 30°. Moreover, an explicit uncertainty analysis for the permittivity is derived, and uncertainties of the extracted complex permittivity are reported.